Fixed Income Securities: Bonds

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1 Economics 173A and Management 183 Financial Markets Fixed Income Securities: Bonds Updated 4/24/17

2 Bonds Debt Security corporate or government borrowing Also called a Fixed Income Security Covenants or Indenture define the contract (this can be, often is, complex); violation initiates a Call. 2 types of Payments: interest principal Interest payments are based on the Coupon Principal payment is the Face

3 Bonds The Coupon is a Percent of the Face: The coupon rate ( CR ). It is fixed by the indenture. It is Not discount rate ( DR ). The Face is the Bond s principal. The amount that will be paid at Term. It is not the market value of the Bond. The Term is the original time of the loan. The Maturity is how long, until what date, until the Face will be paid. At Maturity, the borrower/issuer will pay the Face and the last Coupon payment.

4 Bond Basics Fixed Income Securities: A security such as a bond that pays a specified cash flow over a specific period. Fixed Income Securities vs. Common Stock Fixed Claim High Priority on cash flows Tax Deductible for the borrower Fixed Maturity No Management Control Residual Claim Lowest Priority on cash flows Not Tax Deductible for the borrower Infinite life Management Control Bonds Hybrids (Combinations of debt and equity) Common Stock

5 Bond Analysis Characteristics Types: mortgage, callable, convertible, senior or subordinated, floating rate, zero coupon. Coupon Dates of Coupon Payments Sinking Funds? Credit Rating Pricing present value of future cash flows Yields: Coupon Yield = Coupon / Price YTM = the DR that makes the NPV of CF s = 0 RCYTM = Compound all CFs to Term and do a CAGR Sensitivity to Time, i.e. maturity Sensitivity to changes in interest rates

6 Treasury Bills, Notes, & Bonds Bills 90 days to 6 months Notes 1 year up to 10 years Bonds to 30 years Bond & Note: Face (denomination) of $1,000; quotes in $100 s Bills: Face = $10,000. Discounted and quoted at Yield. Bond & Note: Coupon (rate) paid semi-annually Prices quoted in points (of face) + 1 / 32 No default / credit risk

7 US Treasury Bonds Rates Maturity Month 3.36 % 8.08 % 2 bps 81 bps 6 Month 3.23 % 8.14 % 4 bps 94 bps 2 Year 3.53 % 8.32 % 40 bps 1.21 % 3 Year 3.82 % 8.41 % 87 bps 1.40 % 5 Year 4.41 % 8.44 % 1.69 % 1.77 % 10 Year 4.84 % 8.51 % 2.71 % 2.24 % 30 Year 5.43 % 8.51 % 3.56 % 2.89 %

9 Corporate Bonds Maturity 2/30 spread 2 yrs 5 yrs 10 yrs 30 yrs Jan bps Jan bps Jan bps Jan bps Jan bps Jan bps Jan bps Jan bps Jan bps Jan bps

10 Bond Pricing As with all Financial Assets The price is a Present Value of the expected cash flows discounted at the appropriate (relative to risk) discount (interest) rate.

11 Coupon Payments Relative to other types of securities, bonds produce cash flows that an analyst can predict with a high degree of precision. Fixed rate Variable rate Zero coupons Consols consolidated annuities - perpetuities introduced in 1751.

12 Related Return Concepts APR t n APY CAGR substitute FV Annual Rate r = years = compounding periods: annual =1, monthly =12, daily = 360 Annual Yield = (1 + AAAAAA/nn) nn 1 the APY = APR if n =1 solve for r in Eqn 1: FV=PV(1+r) t = PV(1 + AAAAAA/nn) nnnn = PV(1 + AAAAAA) tt recall that if n=1 then APR = APY

13 Example We invest $ years later we have $150. Calculate the following: Total Return $ 150 HPR ( ) = = 50% Annualized HPR ( /tt )-1 CAGR same as above

14 Bond Pricing DCF Technique P B T t= C t Face t (1 + r) 1 (1 + r) = + T T P B = Price of the bond C t = interest or coupon payments; ordinary annuity portion of the cashflows T = number of periods to maturity r = discount rate F = $ 1,000 paid at Term

15 Bond Pricing: an 8% 10 year Bond at 6%. C t = $ 80 annual annuity F T = $ 1,000 at term T = 10 periods r = 6% (Annual compounding) 10 Σ t =1 P = 80 + B (1+.06) t P B = $1, (1+.06) 10

16 Three Bonds in a 10 percent world Insert Figure 4-6 here.

17 Bond Pricing Zero Coupon Bonds Bond price = PV(principal) = par value ( 1+ r ) T Consols Zero Face, perpetual annuity Bonds anuity cash flow Bond price = PV(annuity) = t t= 1 ( 1+ r) annuity cash flow = r this is capitalizing a cash flow

18 Bond Yields Yield to Maturity: The discount rate that makes the present value of a bond s payments equal to its price, or NPV = 0 or the IRR (internal rate of return) from holding bond till maturity. 3 year bond with interest payment of $100, principal of $1,000; Use Excel Goal Seek to find the DR that makes the PV of the CFS equal to: $1,100 $1,000, and $ 900,

19 RCYTM Holding the Bond to maturity and reinvesting the Coupons: Example 3 year bond with interest payment of $100, Face of $1,000, DR is 10% Calculate the PV of the CFs at 10% Calculate the Future Compounded CFs Calculate the CAGR

20 Bond Yields Prices and Yields (required rates of return) have an inverse relationship When yields get very high the value of the bond will be very low When yields approach zero, the value of the bond approaches the sum of the cash flows

21 Price Yield

22 Bond Risks Price Risks Default risk Interest rate risk Convenience Risks Call risk Reinvestment rate risk Marketability risk

23 Default Risk The income stream from bonds is not riskless unless the investor can be sure the issuer will not default on the obligation. Rating companies Moody s Investor Service Standard & Poor s Duff and Phelps Fitch Kroll

24 Default Risk Rating Categories Investment Grade Bonds Speculative Grade Bonds S&P Moody s Very High Quality AAA, AA Aaa, Aa High Quality A, BBB A, Baa Speculative BB, B Ba, B Very Poor CCC, CC, C, D Caa, Ca, C, D

25 Coupon Yield: YTM: Bond Yields Annual coupon divided by Bond Price. the DR that brings the PV(future CFs) equal to the Bond s Price RCYTM: The CAGR using the Bond Price as the PV and the accumulated, compounded funds at Maturity ( M ) as the FV. Recall that CAGR = TT FFFF PPPP -1

26 Investment Basics When analyzing investment returns, we need a complete transaction, i.e. a full circle investment an open and a close. The Typical Case We OPEN the investment with a Buy at P 0 which we could think of as I 0, the initial investment. We CLOSE the investment with a Sell at P T. Between time = 0 and T, we may need to add interceding Cash Flows any investment proceeds derived from them. Our annualized return is, like the AHPR or CAGR: (P T / P 0 ) (1/T) -1 Simple case

27 Forward Rates term years r at year (1 + r ) = (1 + r ) (1 + r ) (1 + r ) / (1 + r ) = (1 + r ) One-year rate one year from now (1 + r ) = (1 + r ) (1 + r ) (1 + r ) / (1 + r ) = (1 + r ) One-year rate two years from now

Economics 173A and Management 183 Financial Markets

Economics 173A and Management 183 Financial Markets Fixed Income Securities: Bonds Bonds Debt Security corporate or government borrowing Also called a Fixed Income Security Covenants or Indenture define